Final answer:
To find (u∙v)w, calculate the dot product of u and v, then multiply by vector w.
Step-by-step explanation:
To find the expression (u∙v)w, we need to first calculate the dot product of u and v. The dot product of two vectors is found by multiplying their corresponding components and then adding the results. For u = ⟨4,7⟩ and v = ⟨-8,1⟩, the dot product is (4)(-8) + (7)(1) = -32 + 7 = -25.
Next, we multiply the dot product by vector w = ⟨2,-3⟩. Multiplying a scalar (the dot product) by a vector is done by multiplying each component of the vector by the scalar. For (u∙v)w, the result is (-25)(2) = -50 for the x-component and (-25)(-3) = 75 for the y-component.
Therefore, the expression (u∙v)w is equal to the vector ⟨-50, 75⟩.